ASTM E289-99
(Test Method)Standard Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
Standard Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
SCOPE
1.1 This test method covers the determination of linear thermal expansion of rigid solids using either a Michelson or Fizeau interferometer.
1.2 For this purpose, a rigid solid is defined as a material which, at test temperature and under the stresses imposed by instrumentation, has a negligible creep or elastic strain rate, or both, insofar as significantly affecting the precision of thermal length change measurements. This includes metals, ceramics, refractories, glasses, rocks and minerals, graphites and fiber, and other reinforced matrix composites.
1.3 It is recognized that many rigid solids require detailed preconditioning and specific thermal test schedules for correct evaluation of linear thermal expansion behavior for certain material applications. Since a general method of test cannot cover all specific requirements, details of this nature should be discussed in the particular material specifications.
1.4 This test method is applicable to the approximate temperature range -150 to 700°C. The temperature range may be extended depending on the instrumentation and calibration materials used.
1.5 The precision of measurement of this absolute method (better than +40 nm/m[dot]K) is significantly higher than that of comparative methods such as push rod dilatometry (for example, Test Methods D696 and E228) and thermomechanical analysis (for example, Test Method E831) techniques. It is more applicable to materials having low and, or negative coefficients, or both, of expansion (below 5 [mu]m/m[dot]K) and where only very limited lengths or thickness of other higher expansion coefficient materials are available.
1.6 Computer of electronic based instrumentation, techniques and data analysis systems equivalent to this test method can be used. Users of the test method are expressly advised that all such instruments or techniques may not be equivalent. It is the responsibility of the user to determine the necessary equivalency prior to use.
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E 289 – 99
Standard Test Method for
Linear Thermal Expansion of Rigid Solids with
Interferometry
This standard is issued under the fixed designation E 289; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
1.1 This test method covers the determination of linear
thermal expansion of rigid solids using either a Michelson or
2. Referenced Documents
Fizeau interferometer.
2.1 ASTM Standards:
1.2 For this purpose, a rigid solid is defined as a material
D 696 Test Method for Coefficient of Linear Thermal Ex-
which, at test temperature and under the stresses imposed by
pansion of Plastics
instrumentation, has a negligible creep, insofar as significantly
E 220 Test Method for Calibration of Thermocouples by
affecting the precision of thermal length change measurements.
Comparison Techniques
1.3 It is recognized that many rigid solids require detailed
E 228 Test Method for Linear Thermal Expansion of Solid
preconditioning and specific thermal test schedules for correct
Materials with a Vitreous Silica Dilatometer
evaluation of linear thermal expansion behavior for certain
E 473 Terminology Relating to Thermal Analysis
material applications. Since a general method of test cannot
E 831 Test Method for Linear Thermal Expansion of Solid
cover all specific requirements, details of this nature should be
Materials by Thermomechanical Analysis
discussed in the particular material specifications.
E 1142 Terminology Relating to Thermophysical Proper-
1.4 This test method is applicable to the approximate
ties
temperature range − 150 to 700°C. The temperature range may
be extended depending on the instrumentation and calibration
3. Terminology
materials used.
3.1 Definitions:
1.5 The precision of measurement of this absolute method
3.1.1 The following terms are applicable to this document
(better than 640 nm/m·K) is significantly higher than that of
and are listed in Terminology E 473 and E 1142: coefficient of
comparative methods such as push rod dilatometry (for ex-
linear thermal expansion, thermodilatometry, thermomechani-
ample, Test Methods D 696 and E 228) and thermomechanical
cal analysis.
analysis (for example, Test Method E 831) techniques. It is
3.2 Definitions of Terms Specific to This Standard:
applicable to materials having low and either positive or
3.2.1 thermal expansivity, a , at temperature T, is calculated
T
negative coefficients of expansion (below 5 μm/m·K) and
as follows from slope of length v temperature curve:
where only very limited lengths or thickness of other higher
expansion coefficient materials are available. 1 ~L 2 L !
limit 2 1
a 5 5 ~dL/ !/ ~T , T , T ! (1)
T T → T dT L 1 i 2
2 1 i
L
~T 2 T !
1.6 Computer or electronic based instrumentation, tech- i
2 1
niques and data analysis systems equivalent to this test method
and expressed as μm/m·K.
can be used. Users of the test method are expressly advised that
NOTE 1—Thermal expansivity is sometimes referred to as instanta-
all such instruments or techniques may not be equivalent. It is
neous coefficient of linear expansion.
the responsibility of the user to determine the necessary
3.2.2 mean coeffıcient of linear thermal expansion, a , the
equivalency prior to use. m
average change in length relative to the length of the specimen
1.7 This standard does not purport to address all of the
accompanying a change in temperature between temperatures
safety concerns, if any, associated with its use. It is the
T and T , expressed as follows:
responsibility of the user of this standard to establish appro- 1 2
1 ~L 2 L !
2 1
am 5 5 ~DL/ !/ (2)
L0 DT
L T 2 T
~ !
0 2 1
This test method is under jurisdiction of ASTM Committee E-37 on Thermal
Measurements and is the direct responsibility of Subcommittee E37.05 on Thermo-
physical Properties. Annual Book of ASTM Standards, Vol 08.01.
Current edition approved March 10, 1999. Published May 1999. Originally Annual Book of ASTM Standards, Vol 14.03.
published as E 289 – 65 T. Last previous edition E 289 – 94b. Annual Book of ASTM Standards, Vol 14.02.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E 289
where: of flat-uniform thickness pieces of silica or sapphire with the
a is obtained by dividing the linear thermal expansion surfaces partially coated with gold or other high reflectance
m
(DL/L ) by the change of temperature (DT). It is normally
metal. Light, either parallel laser beam (Michelson, see Fig. 2
expressed as μm/m·K.
and Fig. 3) or from a point monochromatic source (Fizeau, see
3.3 Symbols:Symbols:
Fig. 4) illuminates each surface simultaneously to produce a
3.3.1 a 5 mean coefficient of linear thermal expansion,
fringe pattern. As the specimen is heated or cooled, expansion
m
see 3.2.1, /K.
or contraction of the specimen causes a change in the fringe
3.3.2 a 5 expansivity at temperature T, see 3.2.2, / K.
T pattern due to the optical pathlength difference between the
3.3.3 L 5 original length of specimen at temperature T ,
0 0 reflecting surfaces. This change is detected and converted into
mm.
length change from which the expansion and expansion coef-
3.3.4 L 5 length at temperature T , mm.
1 1
ficient can be determined.(1-5)
3.3.5 L 5 length at temperature T , mm.
2 2
3.3.6 DL 5 change in length of specimen between tempera-
5. Significance and Use
tures T and T , nm.
1 2
5.1 Coefficients of linear expansion are required for design
3.3.7 T 5 temperature at which initial length is L , K.
0 0
purposes and are used particularly to determine thermal
3.3.8 T , T 5 two temperatures at which measurements are
1 2
stresses that can occur when a solid artifact composed of
made, K.
different materials may fail when it is subjected to a tempera-
3.3.9 DT 5 temperature difference between T and T , K.
2 1
ture excursion(s).
3.3.10 N 5 number of fringes including fractional parts that
are measured on changing temperature from T to T . 5.2 Many new composites are being produced that have
1 2
3.3.11 l 5 wavelength of light used to produce fringes, very low thermal expansion coefficients for use in applications
v
nm.
where very precise and critical alignment of components is
3.3.12 n 5 index of refraction of gas at reference condition necessary. Push rod dilatometry such as Test Methods D 696,
r
of temperature 288K and pressure of 100 kPa.
E 228, and TMA methods such as Test Methods E 831 are not
3.3.13 n 5 index of refraction of gas at temperature T and
sufficiently precise for reliable measurements either on such
pressure, P.
material and systems, or on very short specimens of materials
3.3.14 n , n 5 index of refractive of gas at temperature T
having higher coefficients.
1 2 1
and T , and pressure, P.
5.3 The precision of the absolute method allows for its use
3.3.15 P 5 average pressure of gas during test, torr.
to:
3.3.16 DL 5 change in length of reference specimen be-
s
5.3.1 Measure very small changes in length;
tween T and T , mm.
1 2
5.3.2 Develop reference materials and transfer standards for
calibration of other less precise techniques;
4. Summary of Test Method
5.3.3 Measure and compare precisely the differences in
4.1 A specimen of known geometry can be given polished
coefficient of “matched” materials.
reflective ends or placed between two flat reflecting surfaces
5.4 The precise measurement of thermal expansion involves
(mirrors). Typical configurations, as shown in Fig. 1, are a
cylindrical tube or a rod with hemispherical or flat parallel ends two parameters; change of length and change of temperature.
or machined to provide a 3-point support. The mirrors consist Since precise measurements of the first parameter can be made
by this test method, it is essential that great attention is also
paid to the second, in order to ensure that calculated expansion
coefficients are based on the required temperature difference.
Thus in order to ensure the necessary uniformity in temperature
of the specimen, it is essential that the uniform temperature
zone of the surrounding furnace or environmental chamber
shall be made significantly longer than the combined length of
specimen and mirrors.
5.5 This test method contains essential details of the design
principles, specimen configurations, and procedures to provide
precise values of thermal expansion. It is not practical in a
method of this type to try to establish specific details of design,
construction, and procedures to cover all contingencies that
might present difficulties to a person not having the technical
knowledge relating to the thermal measurements and general
testing practice. Standardization of the method is not intended
to restrict in any way further development of improved
methodology.
5.6 The test method can be used for research, development,
FIG. 1 Typical Specimen Configurations (a) Michelson Type, (b–d)
Fizeau Type specification acceptance and quality control and assurance.
E 289
FIG. 2 (a) Principle of the Single Pass Michelson Interferometer, (b) Typical Single Pass System
FIG. 3 Typical Double Pass Michelson Interferometer System
FIG. 4 Principle of the Fizeau Interferometer
6. Interferences
6.1 Measurements should normally be undertaken with the
specimen in vacuum or in helium at a low gas pressure in order
The resulting beams are reflected by mirrors M and M and
1 2
to off-set optical drifts resulting from instabilities of the
recombined on B. If M8 is inclined slightly over the light-
refractive index of air or other gases at normal pressures.
beam its mirror image M8 forms a small angle with M
2 1
However, due to the reduced heat transfer coefficient from the
producing fringes of equal thickness located on the virtual face
surrounding environment, measurement in vacuum or low
M8 .
pressure can make actual specimen temperature measurement
7.1.2 One example of a single contact type is shown in Fig.
more difficult. Additional care and longer equilibrium time to
2b. A prism or polished very flat faced cylinder specimen form
ensure that the specimen is at a uniform temperature are
is placed on one mirror with one face also offered to the
necessary.
incident light. An interference pattern is generated and this is
6.2 If vitreous silica flats are used, continuous heating to
divided into two fields corresponding to each end of the
high temperatures may cause them to distort and become
specimen. The lens, L, projects the image of the fringes onto a
cloudy resulting in poor fringe definition.
plane where two detectors are placed one on the specimen and
7. Apparatus
the other on the baseplate fields. As the specimen is heated or
cooled both the specimen and support change length causing
7.1 Interferometer, Michelson Type:
7.1.1 The principle of the single pass absolute system is the surface S and M to move relative to M at different rates.
2 1
The difference in the fringe count provides a measure of the net
shown in Fig. 2a. A parallel light beam usually generated from
a laser through a beam expander is split by a beam splitter B. absolute expansion.
E 289
7.1.3 The principle of the double pass system is essentially
similar to the single pass with three important distinctions. The
specimen can be a relatively simple cylinder with hemispheri-
cal or flat ends and requiring less precise machining, the
interfering beams are reflected twice from each face to the
specimen thus giving twice the sensitivity of the single pass
and no reference arm is required. One example of the double
pass form is shown in Fig. 3.
7.1.4 It is common practice to use polarized laser light and
quarter wave plates to generate circularly polarized light. In
this way detectors combined with appropriate analyzers gen-
erate signals either with information on fringe number, fraction
and motion sense for each beam or linear array data of light
intensity which indicate the profile of the instantaneous whole
fringe pattern. The array data provides complete information
(position of fringe and distance between fringe) to determine
the absolute length change of the specimen depending upon the
system. These signals are normally processed electronically.
7.2 Fizeau Type:
7.2.1 This type is available in both absolute and compara-
tive versions.
7.2.2 The principle of the absolute method is illustrated in
FIG. 5 Typical Furnace
Fig. 4. The specimen is retained between two parallel plates
and illuminated by the point source. Expansion or contraction
of the specimen causes spatial variation between the plates and
radial motion of the circular fringe pattern.
7.2.3 The difference in the fringe counts yields the net
absolute expansion of the specimen.
7.2.4 In practice P is wedge shaped (less than 30 min of
arc) such that light reflected by the upper face is diverted from
the viewing field while the lower face of P is made to absorb
the incident light depending upon the total separation of the
flats.
7.2.5 For use in the comparative mode two forms are
available. These are described in detailed in Annex A1.
7.3 Furnace/Cryostat:
7.3.1 Fig. 5 and Fig. 6 illustrate the construction of a typical
vertical type of furnace and cryostat that are suitable for use in
undertaking these measurements. For the double pass Michel-
son system, horizontal forms of furnace and cryostat can be
used.
7.4 Temperature Measurement System:
7.4.1 The temperature measurement system shall consist of
a calibrated sensor or sensors together with manual, electronic
or equivalent read-out such that the indicated temperature can
be determined better than6 0.5°C.
FIG. 6 Typical Low-Temperature Cryostat
7.4.1.1 Since this method is used over a broad temperature
range, different types of sensors may have to be used to cover
the complete range. The common sensor(s) is a fine gage (32
7.4.1.3 In all cases where thermocouples are used they shall
AWG or smaller wire) or thin foil thermocouples calibrated in be referenced to 0°C by means of an ice water bath or
accordance with Method E 220.
equivalent electronic reference system insulated from the
7.4.1.2 Types E and T are recommended for the temperature effects of temperature variations in the immediate surrounding
range − 190 to 350°C and Types K and S and Nicrosil for ambient.
temperature 0 to 800°C. If Type K is used continuously regular 7.4.1.4 For temperatures below − 190°C a calibrated carbon
checking of the
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